Question

Please help!
Kurt says that you can take the square root of each side of an equation. Therefore, he says that
(x+2)^2 + (9y-5)^2+36 and (x+2) + (y-5)=6 are equivalent equations. Dana says the equations are not equivalent. Who is right? Explain your answer.

Answer 1

you mean (x+2)^2 + (9y-5)^2= 36 or (x+2)^2 + (9y-5)^2+36

Answer 2

?

Answer 3

@Dreaaaaaa

Answer 4

I didn't even notice I put the 9! I meant \[(x+2)^{2}+(y-5)^{2}=36 and (x+2)+(y-5)=6\]

Answer 5

well,first let's work with the second one...

\(\color{lime}{ (x+2)+(y-5)=6 \Longrightarrow ((x+2) + y-5)^2 = 36} \)

Answer 6

Now what?

Answer 7

can u find
\( \large \color{blue}{((x+2) + y-5)^2} \)

Answer 8

i don't know how to start off :/

Answer 9

and sry i missed a bracket :

\( \large \color{blue}{((x+2) + (y-5))^2} \)

Answer 10

ok let's just see what would be \( (a+b)^2 \) you can find it in this way: \( (a+b)(a+b) \)

Answer 11

it would be \( a^2 + b^2 + 2(a+b) \)

Answer 12

so would it be \[x ^{2}+y ^{2}+7\]? Sorry i'm honestly so bad at math haha

Answer 13

no no ... imagine that (x+2) = a and (y-5) = b
and it would be : \(\color{red}{ (x+2)^2 + (y-5)^2 + 2(x+2)(y-5)} \)

Answer 14

so ,\( \color{red}{ (x+2)^2 + (y-5)^2 + 2(x+2)(y-5) = 36} \) but we had \(\large \color{blue}{(x+2)^{2}+(y-5)^{2}=36} \)

Answer 15

so they're not equivalent

Answer 16

got it?

Answer 17

yes! sorry i was trying to write it down and see if i got it haha thank you!